"Solutions to the RH and related mathematical research areas
Disclaimer: with the exception of the last section E all papers of this page are without authorization from the ivory tower
for the latest updated version see http://www.fuchs-braun.com
A. A Kummer function based Zeta function theory
to prove the Riemann Hypothesis
B. A global unique weak H(-1/2) based variational representation of the 3-D Navier-Stokes equation solution & a corresponding solution technique to prove the non-linear Landau damping phenomenon
C. An alternative Schrödinger momentum operator and a related new ground state energy model of the harmonic quantum oscillator enabling a quantum gravity (NMEP) model
We provide a new ground state energy model which ensures convergent quantum oscillator energy series. This enables the definition of a truly infinitesimal geometry based on a non-ordered, still Archimedian field. The corresponding inner product with its induced norm defines the appropriate metric. The (Hilbert space) domains of related self-adjoint, positive definite operators to build appropriate eigenpair structures are built on Cartan´s differential forms. By this, H. Weyl´s "truly" infinitesimal (affine connexions, parallel displacements, differentiable manifolds based) geometry is replaced by a truly infinitesimal (rotation group based) geometry (corresponding to continuous manifolds, only). It is enabled by a new ly proposed H(-1/2) Hilbert space based ground state energy model of the harmonic quantum oscillator:
D. Supporting papers
Braun K., "An alternative quantization of H=xp"
E. PhD thesis
The paper includes a proof of the quasi-optimal approximation behavior of the Ritz-Galerkin method in a Hilbert scale framework. The example 2 gives the model operator of the Symm (Pseudo-Differential) integral operator. Other examples would be the Calderon-Zygmund (singular integral) operator or the Hilbert transform (singular integral) operator.